1. Field of the Invention
This invention relates to electromagnetic flow meters.
2. Prior Art
One conventional flow meter 10 of the electromagnetic type shown in FIG. 1 comprises a fluid-carrying conduit 11 including a pipe 12 of a conductive material and a lining 13 of an insulating material such as polytetrafluoroethylene mounted on the internal surface of the pipe 12. A magnetic field B produced by a magnetic field generating means (shown by a coil) is exerted on the conduit 11 so that an electromotive force E is induced in the fluid 14 flowing through the conduit 11. A pair of diametrically opposed measuring electrodes or probes 15a and 15b are mounted on the conduit 11, and the voltage between the electrodes 15a and 15b is detected to measure the flow rate of the fluid through the conduit 11.
The operation of this conventional electromagnetic flow meter will now be described with reference to an equivalent circuit of the flow meter (FIG. 2). In FIG. 2, E denotes an electromotive force proportional to the flow rate of the fluid, and R.sub.I denotes an internal impedance of the fluid 14, and R.sub.W denotes an impedance representing the total of an impedance at the boundary between the fluid 14 and the conduit 11 and an impedance of the conduit 11. Also, V.sub.M denotes a potential difference between the measuring electrodes 15a and 15b, that is to say, an output voltage of the electromagnetic flow meter. Using this equivalent circuit, the output voltage V.sub.M is represented by the following formula: ##EQU1##
In this case, since the lining 13 is made of an insulating material, the following formula is obtained: EQU R.sub.W &gt;&gt;R.sub.I ( 2)
Then, the following formula is obtained from the formulas (1) and (2): EQU V.sub.M .apprxeq.E (3)
Thus, the output voltage V.sub.M of the electromagnetic flow meter is substantially equal to the electromotive force E proportional to the flow rate of the fluid.
This conventional flow meter 10 of the electromagnetic type have the following disadvantages because of the use of the lining 13:
(a) Since the lining 13 of a uniform thickness has to be mounted on the internal surface of the pipe 12, the manufacture of the flow meter requires much labor and cost.
(b) It is necessary that the lining 13 should have an adequate mechanical strength as well as a corrosion resistance, a wear resistance and a thermal resistance. Therefore, generally, the lining 13 is made of a polymeric material such as polytetrafluoroethylene and rubber. However, the lining made of such a material has failed to meet the above-mentioned requirements satisfactorily.
(c) When a fluid of a conductive nature is deposited on the internal surface of the lining 3, the impedance R.sub.W is lowered so that the formula (2) (R.sub.W &gt;&gt;R.sub.I) is not established. As a result, the formula (3) is also not established so that the output voltage V.sub.M is not proportional to the flow rate of the fluid. Therefore, the flow rate can not be measured accurately.
In order to overcome such disadvantages arising from the use of the lining, there have been proposed electromagnetic flow meters having no lining. One such flow meter 10a is shown in FIGS. 3 and 4, and FIG. 5 shows an equivalent circuit of the flow meter 10a. The electromagnetic flow meter 10a comprises an electrical energy applying means which includes a pair of annular auxiliary electrodes 17a and 17b of copper and a pair of amplifiers 18a and 18b each having a voltage gain of 1. The pair of auxiliary electrodes 17a and 17b are welded to a pipe 12 and surround measuring electrodes or probes 15a and 15b, respectively. The measuring electrode 15a, 15b is connected to one input terminal of the amplifier 18a, 18b while the auxiliary electrode 17a, 17b is connected to the other input terminal of the amplifier 18a, 18b and to the output terminal thereof. With this arrangement, the voltage of the measuring electrode 15a, 15b is rendered equal to the voltage of the auxiliary electrode 17a, 17b. Therefore, as shown in FIG. 5, no current flows through the impedance R.sub.1 between the measuring electrode 15a and the auxiliary electrode 17a and also through the impedance R.sub.2 between the measuring electrode 15b and the auxiliary electrode 17b. Therefore, no current flows through a path constituted by the impedance R.sub.1, the impedance R.sub.W of the pipe 12 and the impedance R.sub.2. As a result, the output voltage V.sub.M of the electromagnetic flow meter 10a is equal to the electromotive force E which is proportional to the flow rate of the fluid 14. In other words, the output voltage V.sub.M of the flow meter is proportional to the flow rate of the fluid 14, so that the flow rate can be measured. The amplifiers 18a and 18b function to cause an output current J to flow through a path extending therebetween and containing the impedance R.sub.W, the output voltage V.sub.M is not affected by the output current J.
Coordinates shown in FIG. 6A indicates the relation between the pipe 12 and a detecting point on the internal surface of the pipe 12 when a magnetic field is applied in a plane perpendicular to the longitudinal axis of the pipe, with the pipe having a uniform thickness. FIG. 6B is a diagrammatic illustration showing the relation between the detecting point and the voltage at the detecting point. The voltage at the detecting point determined by an angle .theta. is indicated by .phi.. A profile of the voltage induced in the fluid 14 at the internal surface of the pipe of the flow meter 10 is shown in a solid line a in the diagrammatic illustration on FIG. 6A. Also, a profile of the voltage produced at the internal surface of the pipe of the flow meter 10a having no lining is shown in a broken line b in the diagrammatic illustration of FIG. 6B. In FIGS. 6A and 6B, the positions of the measuring electrodes 15a and 15b are indicated by .theta.a and .theta.b, respectively. The positions of the auxiliary electrodes 17a and 17b are indicated by .theta.c and .theta.d, respectively. Thus, in the prior art, the flow meter having no lining can properly measure the flow rate of the fluid by causing the cosine wave-shaped voltage profile indicated by the solid line a to approximate the angularly-bent voltage profile indicated by the broken line b. In this case, it is important that the voltage at those portions of the pipe internal surface adjacent to the measuring electrodes 15a and 15b should be equal to the voltage of those portions of the fluids adjacent to said those portions of the pipe internal surface. In other words, in FIG. 6B, the voltage profile a must coincide with the voltage profile b when .theta. is 0.degree. and 180.degree..
In the electromagnetic flow meter 10a, the output current J of a large magnitude is caused to flow through the auxiliary electrodes 17a and 17b welded to the pipe 12, so that voltage drops develop at the welding portions, thereby rendering the measurement of the flow rate inaccurate. This will now be described with reference to FIG. 7 in which V.sub.M denotes the output voltage of the measuring electrode 15a, V.sub.2 denotes the output voltage of the amplifier 18a, V.sub.3 denotes a voltage applied to the auxiliary electrode, and V.sub.4 denotes a voltage of the portion of the pipe 12 adjacent to the measuring electrode 15a. Since the amplifier 18a has a voltage gain of 1, the following formula is obtained: EQU V.sub.M =V.sub.2 =V.sub.3 ( 4)
Thus, the output voltage V.sub.M is equal to the voltage V.sub.3 applied to the auxiliary electrodes 17a. In this condition, output current J of the amplifier 18a flows through the auxiliary electrode 17a into the pipe 12, so that a voltage drop develops at the welded portion between the auxiliary electrode 17a. and the pipe 12. As a result, the voltage V.sub.4 becomes smaller than the voltage V.sub.3 by an amount equal to this voltage drop. Therefore, the following formula is obtained: EQU V.sub.4 &lt;V.sub.3 ( 5)
Further, the following formula is obtained from the formulas (4) and (5): EQU V.sub.4 &lt;V.sub.M ( 6)
Thus, the voltage V.sub.4 of the pipe 12 becomes smaller than the output voltage V.sub.M of the detecting electrode 15a, thereby giving rise to an error in the measurement of the flow rate. As is clear from the foregoing, an accurate measurement of the flow rate can be made when the output voltage V.sub.M of the measuring electrode 15a is equal to the voltage V.sub.4 of the pipe 12.
This phenomenon also occurs at the side of the measuring electrode 15b. In conclusion, in the electromagnetic flow meter 10a in FIG. 3, it is necessary that the output voltage V.sub.M should be equal to the voltage V.sub.4 of the pipe 12 in order to achieve an accurate measurement of the flow rate. Actually, however, by making the output voltage V.sub.M equal to the voltage V.sub.3, it is assumed that the voltage V.sub.M is equal to the voltage V.sub.4. As mentioned above, the voltage profile a coincides with the voltage profile b when .theta. is 0.degree. and 180.degree. (FIG. 6B). However, this can be achieved only when the voltage drops at the welding portions of the auxiliary electrodes 17a and 17b are ignored. With the conventional electromagnetic flow meter, it is impossible that the voltage profile a coincides with the voltage profile b accurately.
U.S. Pat. No. 2,733,604 discloses another electromagnetic flow meter which comprises a pair of probes mounted on a fluid-carrying conduit having no lining, one of the probes being connected to an amplifier in the form of a pentode constituting a cathode follower while the other probe is grounded. The one probe detects a voltage of the fluid in the conduit to send a detecting signal to the amplifier which in turn sends an output voltage through an auto-transformer, which serves to correct the output voltage, to plate-like auxiliary electrodes mounted on the internal surface of the conduit. With this construction, a profile of the voltage of the fluid in the vicinity of the one probe coincides with a profile of the voltage of the auxiliary electrodes. This flow meter is disadvantageous in that the voltage of the one probe and the voltage of the auxiliary electrodes do not coincide with each other when external conditions vary, because no feed-back loop is established. Another disadvantage is that the coincidence of the probe voltage with the auxiliary electrode voltage must be made by manipulating a slider of a variable resistor of the auto-transformer, which is rather troublesome.